Problem: The Looksery company, consisting of n staff members, is planning another big party. Every employee has his phone number and the phone numbers of his friends in the phone book. Everyone who comes to the party, sends messages to his contacts about how cool it is. At the same time everyone is trying to spend as much time on the fun as possible, so they send messages to everyone without special thinking, moreover, each person even sends a message to himself or herself.

Igor and Max, Looksery developers, started a dispute on how many messages each person gets. Igor indicates n numbers, the i-th of which indicates how many messages, in his view, the i-th employee is going to take. If Igor guesses correctly at least one of these numbers, he wins, otherwise Max wins.

You support Max in this debate, so you need, given the contact lists of the employees, to determine whether there is a situation where Igor loses. Specifically, you need to determine which employees should come to the party, and which should not, so after all the visitors send messages to their contacts, each employee received a number of messages that is different from what Igor stated.

Input

The first line contains a single integer n (1 ≤ n ≤ 100) — the number of employees of company Looksery.

Next n lines contain the description of the contact lists of the employees. The i-th of these lines contains a string of length n, consisting of digits zero and one, specifying the contact list of the i-th employee. If the j-th character of the i-th string equals 1, then the j-th employee is in the i-th employee's contact list, otherwise he isn't. It is guaranteed that the i-th character of the i-th line is always equal to 1.

The last line contains n space-separated integers: a1, a2, ..., an (0 ≤ ai ≤ n), where ai represents the number of messages that the i-th employee should get according to Igor.

Output

In the first line print a single integer m — the number of employees who should come to the party so that Igor loses the dispute.

In the second line print m space-separated integers — the numbers of these employees in an arbitrary order.

If Igor wins the dispute in any case, print -1.

If there are multiple possible solutions, print any of them.

Examples

Input

3
101
010
001
0 1 2


Output

1
1 


Input

1
1
1


Output

0



Input

4
1111
0101
1110
0001
1 0 1 0


Output

4
1 2 3 4 

Note

In the first sample Igor supposes that the first employee will receive 0 messages. Since he isn't contained in any other contact list he must come to the party in order to receive one message from himself. If he is the only who come to the party then he will receive 1 message, the second employee will receive 0 messages and the third will also receive 1 message. Thereby Igor won't guess any number.

In the second sample if the single employee comes to the party he receives 1 message and Igor wins, so he shouldn't do it.

In the third sample the first employee will receive 2 messages, the second — 3, the third — 2, the fourth — 3.

Solution (in JAVA):

Solution:
import java.io.BufferedWriter;
import java.util.InputMismatchException;
import java.util.NoSuchElementException;
import java.math.BigInteger;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.io.Writer;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStreamWriter;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Egor Kulikov (egor@egork.net)
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskB solver = new TaskB();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskB {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int count = in.readInt();
        char[][] friends = IOUtils.readTable(in, count, count);
        int[] guess = IOUtils.readIntArray(in, count);
        IntList answer = new IntArrayList();
        while (true) {
            int bad = -1;
            for (int i = 0; i < count; i++) {
                if (guess[i] == 0) {
                    bad = i;
                    break;
                }
            }
            if (bad == -1) {
                break;
            }
            answer.add(bad + 1);
            for (int i = 0; i < count; i++) {
                if (friends[bad][i] == '1') {
                    guess[i]--;
                }
            }
        }
        answer.inPlaceSort();
        out.printLine(answer.size());
        out.printLine(answer);
    }
}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	public int readInt() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	public boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}

	public static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	public char readCharacter() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		return (char) c;
	}

	public interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}

class OutputWriter {
	private final PrintWriter writer;

	public OutputWriter(OutputStream outputStream) {
		writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
	}

	public void print(IntCollection collection) {
		boolean first = true;
		for (IntIterator iterator = collection.iterator(); iterator.isValid(); iterator.advance()) {
			if (first)
				first = false;
			else
				writer.print(' ');
			writer.print(iterator.value());
		}
	}

	public void printLine(IntCollection collection) {
		print(collection);
		writer.println();
	}

	public void close() {
		writer.close();
	}

	public void printLine(int i) {
		writer.println(i);
	}
}

class IOUtils {

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}

	public static char[] readCharArray(InputReader in, int size) {
		char[] array = new char[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readCharacter();
		return array;
	}

	public static char[][] readTable(InputReader in, int rowCount, int columnCount) {
		char[][] table = new char[rowCount][];
		for (int i = 0; i < rowCount; i++)
			table[i] = readCharArray(in, columnCount);
		return table;
	}

}

abstract class IntList extends IntCollection implements Comparable<IntList> {
	private static final int INSERTION_THRESHOLD = 16;

	public abstract int get(int index);
	public abstract void set(int index, int value);

	public IntIterator iterator() {
		return new IntIterator() {
			private int size = size();
			private int index = 0;

			public int value() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				return get(index);
			}

			public void advance() throws NoSuchElementException {
				if (!isValid())
					throw new NoSuchElementException();
				index++;
			}

			public boolean isValid() {
				return index < size;
			}
		};
	}

	private void swap(int first, int second) {
		if (first == second)
			return;
		int temp = get(first);
		set(first, get(second));
		set(second, temp);
	}

	public IntSortedList inPlaceSort() {
		return inPlaceSort(IntComparator.DEFAULT);
	}

	public IntSortedList inPlaceSort(IntComparator comparator) {
		quickSort(0, size() - 1, (Integer.bitCount(Integer.highestOneBit(size()) - 1) * 5) >> 1, comparator);
		return new IntSortedArray(this, comparator);
	}

	private void quickSort(int from, int to, int remaining, IntComparator comparator) {
		if (to - from < INSERTION_THRESHOLD) {
			insertionSort(from, to, comparator);
			return;
		}
		if (remaining == 0) {
			heapSort(from, to, comparator);
			return;
		}
		remaining--;
		int pivotIndex = (from + to) >> 1;
		int pivot = get(pivotIndex);
		swap(pivotIndex, to);
		int storeIndex = from;
		int equalIndex = to;
		for (int i = from; i < equalIndex; i++) {
			int value = comparator.compare(get(i), pivot);
			if (value < 0)
				swap(storeIndex++, i);
			else if (value == 0)
				swap(--equalIndex, i--);
		}
		quickSort(from, storeIndex - 1, remaining, comparator);
		for (int i = equalIndex; i <= to; i++)
			swap(storeIndex++, i);
		quickSort(storeIndex, to, remaining, comparator);
	}

	private void heapSort(int from, int to, IntComparator comparator) {
		for (int i = (to + from - 1) >> 1; i >= from; i--)
			siftDown(i, to, comparator, from);
		for (int i = to; i > from; i--) {
			swap(from, i);
			siftDown(from, i - 1, comparator, from);
		}
	}

	private void siftDown(int start, int end, IntComparator comparator, int delta) {
		int value = get(start);
		while (true) {
			int child = ((start - delta) << 1) + 1 + delta;
			if (child > end)
				return;
			int childValue = get(child);
			if (child + 1 <= end) {
				int otherValue = get(child + 1);
				if (comparator.compare(otherValue, childValue) > 0) {
					child++;
					childValue = otherValue;
				}
			}
			if (comparator.compare(value, childValue) >= 0)
				return;
			swap(start, child);
			start = child;
		}
	}

	private void insertionSort(int from, int to, IntComparator comparator) {
		for (int i = from + 1; i <= to; i++) {
			int value = get(i);
			for (int j = i - 1; j >= from; j--) {
				if (comparator.compare(get(j), value) <= 0)
					break;
				swap(j, j + 1);
			}
		}
	}

	public int hashCode() {
		int hashCode = 1;
		for (IntIterator i = iterator(); i.isValid(); i.advance())
			hashCode = 31 * hashCode + i.value();
		return hashCode;
	}

	public boolean equals(Object obj) {
		if (!(obj instanceof IntList))
			return false;
		IntList list = (IntList)obj;
		if (list.size() != size())
			return false;
		IntIterator i = iterator();
		IntIterator j = list.iterator();
		while (i.isValid()) {
			if (i.value() != j.value())
				return false;
			i.advance();
			j.advance();
		}
		return true;
	}

	public int compareTo(IntList o) {
		IntIterator i = iterator();
		IntIterator j = o.iterator();
		while (true) {
			if (i.isValid()) {
				if (j.isValid()) {
					if (i.value() != j.value()) {
						if (i.value() < j.value())
							return -1;
						else
							return 1;
					}
				} else
					return 1;
			} else {
				if (j.isValid())
					return -1;
				else
					return 0;
			}
			i.advance();
			j.advance();
		}
	}

}

class IntArrayList extends IntList {
	private int[] array;
	private int size;

	public IntArrayList() {
		this(10);
	}

	public IntArrayList(int capacity) {
		array = new int[capacity];
	}

	public int get(int index) {
		if (index >= size)
			throw new IndexOutOfBoundsException();
		return array[index];
	}

	public void set(int index, int value) {
		if (index >= size)
			throw new IndexOutOfBoundsException();
		array[index] = value;
	}

	public int size() {
		return size;
	}

	public void add(int value) {
		ensureCapacity(size + 1);
		array[size++] = value;
	}

	public void ensureCapacity(int newCapacity) {
		if (newCapacity > array.length) {
			int[] newArray = new int[Math.max(newCapacity, array.length << 1)];
			System.arraycopy(array, 0, newArray, 0, size);
			array = newArray;
		}
	}

}

abstract class IntCollection {
	public abstract IntIterator iterator();
	public abstract int size();
	public abstract void add(int value);

}

abstract class IntSortedList extends IntList {
	protected final IntComparator comparator;

	protected IntSortedList(IntComparator comparator) {
		this.comparator = comparator;
	}

	public void set(int index, int value) {
		throw new UnsupportedOperationException();
	}

	public void add(int value) {
		throw new UnsupportedOperationException();
	}

	public IntSortedList inPlaceSort(IntComparator comparator) {
		if (comparator == this.comparator)
			return this;
		throw new UnsupportedOperationException();
	}

	protected void ensureSorted() {
		int size = size();
		if (size == 0)
			return;
		int last = get(0);
		for (int i = 1; i < size; i++) {
			int current = get(i);
			if (comparator.compare(last, current) > 0)
				throw new IllegalArgumentException();
			last = current;
		}
	}

}

interface IntIterator {
	public int value() throws NoSuchElementException;
	public void advance() throws NoSuchElementException;
	public boolean isValid();
}

interface IntComparator {
    public static final IntComparator DEFAULT = new IntComparator() {
        public int compare(int first, int second) {
            if (first < second)
                return -1;
            if (first > second)
                return 1;
            return 0;
        }
    };

	public int compare(int first, int second);
}

class IntSortedArray extends IntSortedList {
	private final int[] array;

	public IntSortedArray(IntCollection collection, IntComparator comparator) {
		super(comparator);
		array = new int[collection.size()];
		int i = 0;
		for (IntIterator iterator = collection.iterator(); iterator.isValid(); iterator.advance())
			array[i++] = iterator.value();
		ensureSorted();
	}

	public int get(int index) {
		return array[index];
	}

	public int size() {
		return array.length;
	}
}